Average is a basic concept and averaging is a basic technique/tool behind the most of the measures associated to characteristics of data. A number of definitions/formulations of average have been developed so far. These definitions/formulations have been found suitable to be used in different situations. There are still many situations where there are scarcities of definitions/formulations of average to deal with the respective situations. It has been found possible to compose general definition of average so that the definitions/formulations of average, already developed, can be obtained/derived from it as well as more new definitions/formulations of average can be obtained/derived from it. One general definition of average, termed in this paper as Generalized fG -Mean, has been introduced with a view to obtain different definitions/formulations of average. Applying the technique, some definitions/formulations have been derived for various types of averages. This paper describes this general definition and the derivation of a number of definitions/formulations of average.

Keywords

Average, Generalized fG -Mean, Existing Means, Derivations

Reference

[01]

Bakker Arthur (2003): “The early history of average values and implications for education”, Journal of Statistics Education, 11 (1), 17-26.

[02]

John Bibby (1974): “Axiomatisations of the average and a further generalisation of monotonic sequences”, GlasgowMathematical Journal, 15, 63–65.

Dhritikesh Chakrabarty (2018): “Derivation of Some Formulations of Average from One Technique of Construction of Mean”, American Journal of Mathematical and Computational Sciences, 3 (3), 62 – 68. Available in http://www.aascit.org/journal/ajmcs.

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